Step by step
The question
Question: A bike costs $230 with a 15% tax.
What was the price before tax?
1 Find what we know
What do we know?
A 15% tax is added on top.
With the tax: $230.
What do we want?
The price before.
2 Name the unknown
We don't know the price before.
So we call it x.
The tax is 15% of it.
15% means 15 out of 100.
That is 3 out of 20.
So the tax is 3 times x, divided by 20: 3x/20.
3 Write the equation
In words: the price before, plus the tax, is the price with tax.
So the equation is x + 3x/20 = 230.
Now we solve it.
4 Remove the fraction
The bottom number is 20.
Times 20 will remove it.
We multiply every part by 20.
We do it on both sides, so they stay equal.
20 divided by 20 is 1.
Write what is left.
Do the multiplications.
No more fractions!
5 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
20x + 3x = 23x.
Now we have 23x = 4600.
6 Remove the 23
23x means 23 times x.
We want just x.
To remove times 23, we divide by 23.
We do it on both sides, so they stay equal.
23 divided by 23 is 1.
So just x is left.
4600 divided by 23 is 200.
So x = 200!
7 Answer the question
So the price before was $200.
8 Check
Let's check in the story.
The tax: 15% of $200.
$200 divided by 20 is $10.
Times 3 is $30.
$200 plus $30 is $230, like the story says.
Does it make sense?
The price went up.
So the price before, $200, is less than $230.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.